Historically, transmission transfer capability between transmission systems was typically assumed based on the thermal limits of specific transmission paths. Because electric transmission systems are becoming more and more heavily loaded, accurately evaluating transfer capability between transmission systems and maintaining minimum levels of transfer capability has become increasingly important. This Thesis evaluates the transfer capability needs and limitations of a specific small electric utility. Identified are various analysis tools and evaluation methods used to determine transfer capability. Two specific evaluation methods are analyzed and compared to determine the best method of determining transfer capability. Various solutions, including upgrading existing or installing new transmission interconnections, are identified and evaluated to determine the best overall solution to achieve and maintain the utility?s desired transfer capability level.

We develop well-posedness theory and analytical and numerical solution techniques for Boussinesq-type equations. Firstly, we consider the Cauchy problem for a generalized Boussinesq equation. We show that under suitable conditions, a global solution for this problem exists. In addition, we derive sufficient conditions for solution blow-up in finite time. / Secondly, a generalized Jacobi/exponential expansion method for finding exact solutions of non-linear partial differential equations is discussed. We use the proposed expansion method to construct many new, previously undiscovered exact solutions for the Boussinesq and modified Korteweg-de Vries equations. We also apply it to the shallow water long wave approximate equations. New solutions are deduced for this system of partial differential equations. / Finally, we develop and validate a numerical procedure for solving a class of initial boundary value problems for the improved Boussinesq equation. The finite element method with linear B-spline basis functions is used to discretize the equation in space and derive a second order system involving only ordinary derivatives. It is shown that the coefficient matrix for the second order term in this system is invertible. Consequently, for the first time, the initial boundary value problem can be reduced to an explicit initial value problem, which can be solved using many accurate numerical methods. Various examples are presented to validate this technique and demonstrate its capacity to simulate wave splitting, wave interaction and blow-up behavior.

The main objectives of this research are (a) to develop advanced simulation methods for voltage-recovery phenomena using improved, realistic system models and accurate solution techniques and (b) to develop methods for the mitigation of problems related to slow voltage recovery. Therefore, this work concentrates on the areas of voltage-recovery analysis in electric power systems, dynamic load modeling with emphasis on induction-motor models, dynamic simulation with emphasis on the numerical integration methods, and optimal allocation and operation of static and dynamic VAr resources. In the first part of this work, a general framework for power-system analysis is presented the main characteristics of which are (a) the utilization of full three-phase models and (b) the use of a "quadratized" mathematical formulation, which models the system under study as a set of mathematical equations of order no more than two. The modeling approach is essentially the same for steady-state, quasi-steady-state, and dynamic analysis. Furthermore, a new approach for time-domain transient simulation of electric power systems and dynamical systems, in general, is introduced in this research. The new methodology has been named quadratic integration method. The method is based on a numerical integration scheme that assumes that the system states vary quadraticaly within an integration time step. Accurate modeling and simulation of voltage-recovery phenomena allows the development of mitigation methodologies via the optimal allocation and operation of static and dynamic VAr resources over the planning horizon. This problem is solved with successive dynamic programming techniques with the following two innovations: (a) the states at each stage (candidate solutions) are obtained with static and dynamic (trajectory) sensitivity analysis and (b) each candidate solution is evaluated by considering the optimal operation of installed static and dynamic VAr sources utilizing concepts from the theory of applied optimal control and trajectory optimization.